When copying a previously created SharePoint site to another SharePoint site, an error was shown of:

List does not exist

The page you selected contains a list that does not exist.  It may have been deleted by another user.

Because the browser instance of the SharePoint site described nothing about the error other than the general message shown above, SharePoint Designer was used to see which webpart was causing the issue.  This webpart was able to be deleted and the new site rendered correctly.